# Chapter 2

## Hugh Lassen

The introduction of geometry in this chapter invites the reader to consider the formula for doubling (2 dimensions - 2 to the 2nd, 3, 2 to the third, 4, 2 to the 4.) The reader then begins to imagine what one could call the "space" that a fourth dimensional object occupies. The chapter then goes on to describe the space taken up by a square based pyramid occupying one third the area of a square.

At this point I decided to construct three square based pyramids to attempt to identify their properties and visualize what they might look like in four space. This turned out to be interesting as I needed to use the basic yet rusty algebra to discern the diagonals. Having constructedthe model while not taking into account the 1/8th inch insulated wire, I ran into a few problems. It ended up looking alright but, it didn't fit together exactly correctly. It might be interesting, although I ran out of time, to account for this in the model. Ambitiously I had planned to project each slice into the fourth dimension- however, that proved far more complicated than I expected.

As I read on I discovered that I was barking up the wrong tree as one might say. One needs to reduce the three dimensional off - center pyramid into two dimensions in order to visualise what a four dimensional object will look like in three. This technique opens up many new ways of thinking about the fourth dimension. For example as prof. B mentioned in class the three dimentional polyhedral must fold to one point, but where? and how?

The sub chapter - The Volume of an Incomplete Pyramid was also interesting and all the way through I wished that there was an example that contained numbers to refer to. Would it be possible to have an exercise that asks the reader to compute the missing volume of an incomplete pyramid? For someone on a lower mathematical level providing examples helps loads.

After grapling with attempting to visualize or conceptualize the fourth dimension the reader discovers the "Fractal." One understands the concept however the implications and applications seem a little baffling? I guess that'l become clear over time.